Munira Raja mraja@liv.ac.uk

Organic Electronics Group Department of Electrical Engineering & Electronics

MOS-AK/GSA ESSDERC/ESSCIRC Workshop, Bordeaux, 21st Sept 2012

Motivation §  Organic Electronics is rapidly emerging technology for flexible, high volume

and low-cost systems i.e. RFID tags, Displays, Smart sensors (e.g. SIMS)

§  SIMS is focused in detection of cholesterol levels in human blood however will provide platform in industrial and environmental testing

§  SIMS integrates nanosensor, organic circuitry, printed battery and printed display on a same flexible substrate

Biosensor

Battery

Display

Circuit

Polycrystalline - Background theory §  Polycrystalline consists of arrays of ordered

grains separated by disordered grain boundaries

§  Grain (of width 2a) is treated as a single crystal i.e. EF moves freely compared to boundaries

§  Grain boundaries comprise of large density of traps which results in pinning of the EF thereby limiting the conduction

§  The traps are assumed to comprise of density of states (DOS) similar to that of disordered material, which follows an exponential distribution

§  The edge of ELUMO (assuming n-type) dips at centre and extent of the dip depends on relative size of effective Debye length3 (intrinsic material) or depletion region (doped material). At minimal point, the concentration of electron is at the highest

3 M. Raja and W. Eccleston, J. Appl. Phys. 110, 114524, (2011)

Diffusion mechanism §  Diffusion mechanism is dominant at low voltages

§  There is no potential drop between adjacent grain boundaries and/or across the channel i.e. between the source and drain contacts

§  The energy difference between ELUMO minimum and EF changes between adjacent grains

§  Carrier density decreases at grain centres down the channel

n2 n3 n1

n1 > n2 > n3

2a

S O U R C E

D R A I N

2a 2a

Drift mechanism §  Drift mechanism is dominant at higher voltages

§  There is a net potential drop between adjacent grains (i.e. V = 2aFxmean) however no change in the position of EF with respect to ELUMO minimum

§  Carrier density is constant (at grain centre)

§  Conduction down the channel is enhanced due to lowering of the barriers as a result of an applied drain voltage

n

n

n

D R A I N

S O U R C E

(x-2a) (x) (x+2a)

Diffusion and Drift mechanisms §  Upon application of gate and drain biases, the various fluxes FX flowing

across the grain boundaries are determined,

diffusion (Fdiffusion) drift (Fdrift)

§  The resultant total fluxes at equilibrium is found to follow:

(x-2a) (x) (x+2a)

D R A I N

S O U R C E

z

x

Drain Current models §  Currents expressions are obtained by integrating individual fluxes over the

depth of channel (in z-direction) so as to include total accumulated charge:

§  The expression for field strength FZ is obtained by solving Poisson’s equation as:

§  Assuming the density of traps at the grain boundary to be given as:

§  Where TC is characteristic temperature associated with degree of disorder

Drain Current models §  Consequently, the drain current expressions4 in terms of applied gate and

drain voltages under diffusion and drift are given as:

4 M. Raja et. al, in Print JAP

Where Cox is gate capacitance, W and L are channel width and length, a is half grain size, ν is frequency of attempted jumps, No is density of traps at boundary, εb is relative permittivity of OSC, Tc characteristics temperature and c = 4Tc/T – 1 (in diffusion) and 2Tc/T – 1 (in drift)

Kdrift

Kdiffusion

Parameter Extraction (I)

§  For validation of the model, respective parameters i.e. Kdrift, Kdiffusion, cdrift and cdiffusion need to be extracted from experimental data i.e. sub-threshold plots of TIPS OTFT. This initially requires to extract threshold voltages VT

 

-40 -30 -20 -10 0 1010-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

DriftDiffusion

VD = - 1V VD = - 5V VD = - 40V

W = 2 mm, L = 100 µm

Dra

in C

urre

nt, I D

(A

)

Gate Voltage, VG (V)

Bulk leakage

Sub-threshold plots of TIPS OTFT

§  Respective values of VT are extracted in:

i.  Diffusion Region Requires multiple transfer plots at low VD, with no dependency on VG

ii.  Drift Region In this region, drift current dominates. More dependency on VG i.e. transfer plots begin to separate

Parameter Extraction (II) §  Using respective values of VT,

values of K and c (or TC) were extracted from derivatives of current expressions as below:

 

0.7 0.8 0.9 1.0

-11.0

-10.8

-10.6

-10.4

-10.2

-10.0 Experimental data Linear Fit

log

[dI D

/d(V

GS- V

Tdiff)]

(A

V-1)

log (VGS- VTdiff) (V)

 

0.4 0.6 0.8 1.0 1.2 1.4 1.6

-9

-8

-7

-6 Experimental data Linear fit

log

[dI D

/d(V

GS- V

Tdrif

t)]

(AV-1

)

log (VGS- VTdrift) (V)

Diffusion

Drift

VT 11 V - 4 V

K 1 × 10-14

(SI unit) 7.2 × 10-12 (SI unit)

c 4.18 2.77

Tc 777 K 566 K

MNE (kTC/q)

67.34 meV 49 meV

Validation of the Polycrystalline model

-40 -30 -20 -10 0 100

1

2

3

Dra

in C

urre

nt,

I D

(µA

)

Gate Voltage, VGS (V)

Experimental data Polcrystalline model

a) VDS= -5 V

10-12

10-10

10-8

10-6

Dra

in C

urre

nt,

I D (

A)

 

-40 -30 -20 -10 0 100

2

4

6

Dra

in C

urre

nt,

I D

(µA

)

Gate Voltage, VGS (V)

Experimental data Polycrystalline model

b) VDS= -40 V

10-12

10-10

10-8

10-6

Dra

in c

urre

nt,

I D

(A)

 

-40 -30 -20 -10 00.0

0.1

0.2

0.3

0.4

0.5 Experimental data Polycrystalline model

VGS = -10 V

Dra

in C

urre

nt,

I D

(µA)

Drain Voltage, VDS (V)

VGS = -20 V(a)

 

-40 -30 -20 -10 0

0

2

4

6

8 Experimental data Polycrystalline model

VGS = -10 V

VGS = -20 V

VGS = -30 V

Dra

in C

urre

nt,

I D

(µA)

Drain Voltage, VDS (V)

VGS = -40 V(b)

Significance of Mobility in Polycrystalline devices

§  Assume a crystalline and disordered materials to be in direct contact (ignoring work function difference and trapping effects) such as:

§  Subsequently, at thermal equilibrium the carrier fluxes between the two materials are equal and thus:

Significance of Mobility in Polycrystalline device

§  Substitute for carrier concentration,

§  The measured effective mobility contains additional pre-factor but with carrier dependency similar to the Universal Mobility Law 5-6

§  Then,

5 A. R. Brown, D. M. de Leeuw, E. E. Havinga and A. Pomp, Synth. Met. 68 (1), 65 (1994). 6 C. P. Jarret, R. H. Friend, A. R. Brown and D. M. de Leeuw, J. Appl. Phys. 77 (12), 6289 (1995).

Universal Mobility Law §  Carrier concentration increases due to doping or field-effects effects §  Doping of disordered semiconductor with DDQ7 in solution resulted in

increase in mobility for small changes in dopant (or carrier) concentration

7 M. Raja et. al. J. Appl. Phys. 92 (3), 1441, 2002

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-110-12

10-11

10-10

10-9

10-8

10-7

PTAA

P3HT

Bul

k m

obili

ty,

µ

(m2 V

-1s-1

)

Conductivity, σ (Sm-1)

m = 2, TC = 900 K and MNE = 78 meV

Effective Mobility Vs. Gate voltage §  In terms of applied gate voltage, the effective mobility increases with

increase in VG, to a power exponent dependent on TC (i.e. degree of disorder)

 

-40 -30 -20 -10 00.0

0.2

0.4

0.6

Effe

ctiv

e dr

ift m

obili

ty, µ eff

(cm

2 V-1s-1

)

Gate Voltage, VGS (V)

TC (drift) = 566 K

Disordered Vs. Polycrystalline §  Comparing drift currents for Disordered8 and Polycrystalline OTFTs below :

and

§  The equations are similar (i.e. power exponent of TC on applied voltages) possibly because the surface potential due to gate bias is affected by EF pinning in the grain boundaries which are disordered in nature

where and

8 M. Raja and W. Eccleston, IET Circ. Dev. Syst. 6 (2), 122, (2012)

Disordered Vs. Polycrystalline §  For TIPS OTFT data, the polycrystalline model fits better than disordered

model particularly at low voltages where diffusive component is dominant

§  Disordered model assumes a drift mechanism only thus a power exponent of 2Tc/T across the whole range of the applied voltage. Note for the diffusive component in polycrystalline the power exponent is 4TC/T - 1

 

-40 -30 -20 -10 0 100

2

4

6

8

10

Experimental data Polycrystaline model Disordered model

Dra

in C

urre

nt,

I D

(µA

)

Gate Voltage, VGS (V)

(b)

10-13

10-11

10-9

10-7

10-5

Dra

in C

urre

nt,

I D

(A)

 

-40 -30 -20 -10 0 100

1

2

3

4

5

Experimental data Polycrystaline model Disordered model

Dra

in C

urre

nt,

I D

(µA)

Gate Voltage, VGS (V)

10-13

10-11

10-9

10-7

10-5

Dra

in C

urre

nt, I D

(A

)

(a)

Conclusions §  Polycrystalline OTFT model was developed, taking into account various

modes of conduction i.e. diffusion and drift, and expressed in terms of essential parameters i.e. grain sizes, characteristic temperature

§  Polycrystalline OTFT model showed good agreement with experimental data of TIPS Pentacene OTFT

§  Similar dependency of the effective mobility on carrier concentration was observed in polycrystalline to disordered materials. Further studies show similar power dependencies of the applied voltages on both OTFT models

§  However better fits to the experimental data are attained with the Polycrystalline rather than Disordered model due to the presences of the diffusive component at low voltages

§  For complete compact models, other effects such as contact resistance need to be included, and also transient models developed

Acknowledgments

Bill Eccleston, David Donaghy, Robert Myers, Sidra Afzal, Grace Carradice, Lin Sheng and Paul Rimmer